Prioritizing modifiers between different objects
Not directly.

If a modifier (e.g. Am1) takes another object (B) as input, it will use the result of all modifiers applied to that object (i.e. it will depend on Bm1 and Bm2). 

If you need a modifier on one object that only uses some of the modifiers on another (e.g B + Bm1) then you need to make a copy of that object with only the modifiers you need. 

If you make the copy using Alt+D rather than Shift+D then both objects will share the same mesh, so any edits on one will update the other.